<h2>题目编号 : 154</h2>
<div style="color:#666;font-size:80%;">12 May 2007</div><br />
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<p>A triangular pyramid is constructed using spherical balls so that each ball rests on exactly three balls of the next lower level.</p>
<div style="text-align:center;"><img src="project/images/p_154_pyramid.gif" width="488" height="379" alt="" /></div>
<p>Then, we calculate the number of paths leading from the apex to each position:</p>
<p>A path starts at the apex and progresses downwards to any of the three spheres directly below the current position.</p>
<p>Consequently, the number of paths to reach a certain position is the sum of the numbers immediately above it (depending on the position, there are up to three numbers above it).</p>
<p>The result is <i>Pascal's pyramid</i> and the numbers at each level <var>n</var> are the coefficients of the trinomial expansion 
(<var>x + y + z</var>)<img src="" style="display:none;" alt="^(" /><sup><var>n</var></sup><img src="" style="display:none;" alt=")" />.</p>
<p>How many coefficients in the expansion of (<var>x + y + z</var>)<img src="" style="display:none;" alt="^(" /><sup>200000</sup><img src="" style="display:none;" alt=")" /> are multiples of 10<img src="" style="display:none;" alt="^(" /><sup>12</sup><img src="" style="display:none;" alt=")" />?</p>
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